Area and Volume
The surface area A and the volume V of a regular octahedron of edge length a are:
Thus the volume is four times that of a regular tetrahedron with the same edge length, while the surface area is twice (because we have 8 vs. 4 triangles).
If an octahedron has been stretched so that it obeys the equation:
The formula for the surface area and volume expand to become:
Additionally the inertia tensor of the stretched octahedron is:
These reduce to the equations for the regular octahedron when:
Read more about this topic: Octahedron
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